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# Program to compare m^n and n^m

• Difficulty Level : Easy
• Last Updated : 12 May, 2021

Given two positive integers m and n, the task is to write a program that checks whether m^n is greater than, less than or equal to n^m.
Examples :

Input: m = 3, n = 10
Output: m^n > n^m
Explanation : 3^10=59049 which is greater than 10^3=1000
Input: m = 987654321, n = 123456987
Output: m^n < n^m

A naive approach is to compute m^n and n^m, which causes overflow when m and n are very large.
An efficient approach is to solve this problem using log

Given LHS = m^n and RHS = n^m.
After taking log on both sides, LHS = n*log(m) and RHS = m*log(n)
Then compare the LHS and RHS.

## C++

 `// CPP program to compare which is greater``// m^n or n^m ``#include ``using` `namespace` `std;` `// function to compare m^n and n^m``void` `check(unsigned ``long` `long` `m, unsigned ``long` `long` `int` `n)``    ``{``        ``// m^n``        ``double` `RHS = m * (``double``)``log``(n);``        ` `        ``// n^m``        ``double` `LHS = n * (``double``)``log``(m);``        ` `        ``if` `( LHS > RHS )``            ``cout << ``"m^n > n^m"``;``            ` `        ``else` `if` `( LHS < RHS )``            ``cout << ``"m^n < n^m"``;``            ` `        ``else``            ``cout << ``"m^n = n^m"``;``    ``}` `// Drivers Code``int` `main() {``    ` `    ``unsigned ``long` `long` `m = 987654321, n = 123456987;``    ` `    ``// function call to compare m^n and n^m``    ``check(m, n);``    ` `    ``return` `0;``}`

## Java

 `// Java program to compare which``// is greater m^n or n^m``import` `java .io.*;` `class` `GFG``{``// function to compare``// m^n and n^m``static` `void` `check(``long` `m, ``long` `n)``{``    ``// m^n``    ``double` `RHS = m * (``double``)Math.log(n);``    ` `    ``// n^m``    ``double` `LHS = n * (``double``)Math.log(m);``    ` `    ``if` `(LHS > RHS)``        ``System.out.print(``"m^n > n^m"``);``        ` `    ``else` `if` `(LHS < RHS)``    ``System.out.print(``"m^n < n^m"``);``        ` `    ``else``        ``System.out.print(``"m^n = n^m"``);``}` `// Driver Code``static` `public` `void` `main (String[] args)``{``    ``long` `m = ``987654321``, n = ``123456987``;` `    ``// function call to``    ``// compare m^n and n^m``    ``check(m, n);``}``}` `// This code is contributed by anuj_67.`

## Python3

 `# Python3 program to compare``# which is greater m^n or n^m``import` `math` `# function to compare``# m^n and n^m``def` `check( m, n):``    ` `    ``# m^n``    ``RHS ``=` `m ``*` `math.log(n);``    ` `    ``# n^m``    ``LHS ``=` `n ``*` `math.log(m);``    ` `    ``if` `(LHS > RHS):``        ``print``(``"m^n > n^m"``);``        ` `    ``elif` `(LHS < RHS):``        ``print``(``"m^n < n^m"``);``        ` `    ``else``:``        ``print``(``"m^n = n^m"``);` `# Driver Code``m ``=` `987654321``;``n ``=` `123456987``;` `# function call to``# compare m^n and n^m``check(m, n);` `# This code is contributed by mits`

## C#

 `// C# program to compare which ``// is greater m^n or n^m``using` `System;` `class` `GFG``{``// function to compare``// m^n and n^m``static` `void` `check(``ulong` `m, ``ulong` `n)``{``    ``// m^n``    ``double` `RHS = m * (``double``)Math.Log(n);``    ` `    ``// n^m``    ``double` `LHS = n * (``double``)Math.Log(m);``    ` `    ``if` `(LHS > RHS)``        ``Console.Write(``"m^n > n^m"``);``        ` `    ``else` `if` `(LHS < RHS)``    ``Console.Write(``"m^n < n^m"``);``        ` `    ``else``        ``Console.Write(``"m^n = n^m"``);``}` `// Driver Code``static` `public` `void` `Main ()``{``    ``ulong` `m = 987654321, n = 123456987;` `    ``// function call to``    ``// compare m^n and n^m``    ``check(m, n);` `}``}` `// This code is contributed by anuj_67.`

## PHP

 ` ``\$RHS` `)``        ``echo` `"m^n > n^m"``;``        ` `    ``else` `if` `( ``\$LHS` `< ``\$RHS` `)``    ``echo` `"m^n < n^m"``;``        ` `    ``else``        ``echo` `"m^n = n^m"``;``}` `// Driver Code``\$m` `= 987654321;``\$n` `= 123456987;` `// function call to``// compare m^n and n^m``check(``\$m``, ``\$n``);` `// This code is contributed by anuj_67.``?>`

## Javascript

 ``

Output :

`m^n < n^m`

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